Stability of infinite dimensional stochastic evolution equations with memory and Markovian jumps

Jiaowan Luo and Kai Liu

Stochastic Processes and their Applications, 2008, vol. 118, issue 5, 864-895

Abstract: A strong solutions approximation approach for mild solutions of stochastic functional differential equations with Markovian switching driven by Lévy martingales in Hilbert spaces is considered. The Razumikhin-Lyapunov type function methods and comparison principles are studied in pursuit of sufficient conditions for the moment exponential stability and almost sure exponential stability of equations in which we are interested. The results of [A.V. Svishchuk, Yu.I. Kazmerchuk, Stability of stochastic delay equations of Itô form with jumps and Markovian switchings, and their applications in finance, Theor. Probab. Math. Statist. 64 (2002) 167-178] are generalized and improved as a special case of our theory.

Keywords: Infinite; dimensional; stochastic; evolution; equations; with; memory; Lévy; processes; Markovian; jumps; Moment; exponential; stability; Almost; sure; exponential; stability (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (4)

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